Optimization algorithms on matrix manifolds Hessian Riemannian gradient flows in convex programming, SIAM J. Control Optim, vol.43, issue.22, pp.477-501, 2004. ,
Singular Riemannian barrier methods and gradient-projection dynamical systems for constrained optimization, Optimization, vol.314, issue.5-6, pp.5-6435, 2004. ,
DOI : 10.1090/S0002-9904-1967-11761-0
Interior Gradient and Proximal Methods for Convex and Conic Optimization, SIAM Journal on Optimization, vol.16, issue.3, pp.697-725, 2006. ,
DOI : 10.1137/S1052623403427823
Optimal control and viscosity solutions of Hamilton- Jacobi-Bellman equations. Systems & Control: Foundations & Applications, With appendices by Maurizio Falcone and Pierpaolo Soravia, 1997. ,
The nonlinear geometry of linear programming. I. Affine and projective scaling trajectories, Trans. Amer. Math. Soc, vol.314, issue.2, pp.499-526, 1989. ,
Deterministic state-constrained optimal control problems without controllability assumptions. ESAIM: Control, Optimization and Calculus of Variations, pp.995-1015, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00415953
Barrier Operators and Associated Gradient-Like Dynamical Systems for Constrained Minimization Problems, SIAM Journal on Control and Optimization, vol.42, issue.4, pp.1266-1292, 2003. ,
DOI : 10.1137/S0363012902410861
Convex functions of Legendre type in general Banach spaces, J. Convex Analysis, vol.8, issue.2, pp.569-582, 2001. ,
Convex functions: constructions, characterizations and counterexamples, 2010. ,
DOI : 10.1017/CBO9781139087322
Optimal syntheses for control systems on 2-D manifolds, 2004. ,
Full convergence of the steepest descent method with inexact line searches, Optimization, vol.32, issue.2, pp.137-146, 1995. ,
DOI : 10.1007/BF01071091
Optimal control problems on manifolds: a dynamic programming approach, Journal of Mathematical Analysis and Applications, vol.287, issue.1, pp.118-140, 2003. ,
DOI : 10.1016/S0022-247X(03)00535-3
Nonsmooth Analysis and Control Theory, 1998. ,
URL : https://hal.archives-ouvertes.fr/hal-00863298
Hamilton-Jacobi characterization of the state constrained value. Nonlinear Analysis: Theory, Methods & Applications, pp.725-734, 2005. ,
A relationship between the second derivatives of a convex function and of its conjugate, Mathematical Programming, vol.260, issue.1, pp.364-365, 1977. ,
DOI : 10.1007/BF01584350
Riemannian Geometry, Birkhäuser Boston, 1992. ,
DOI : 10.1007/978-1-4757-2201-7
Perturbed variations of penalty function methods, Annals of Operations Research, vol.14, issue.2, pp.371-380, 1990. ,
DOI : 10.1007/BF02055202
Discontinuous solutions of Hamilton???Jacobi???Bellman equation under state constraints, Calculus of Variations and Partial Differential Equations, vol.22, issue.3-4, pp.3-4725, 2013. ,
DOI : 10.1007/s00526-012-0501-8
URL : https://hal.archives-ouvertes.fr/hal-00710717
Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems, Journal of Optimization Theory and Applications, vol.35, issue.1, pp.20-40, 2000. ,
DOI : 10.1023/A:1004668504089
Infinite horizon problems on stratifiable state-constraints sets, Journal of Differential Equations, vol.258, issue.4, pp.1430-1460, 2015. ,
DOI : 10.1016/j.jde.2014.11.001
URL : https://hal.archives-ouvertes.fr/hal-00955921
Central Paths, Generalized Proximal Point Methods, and Cauchy Trajectories in Riemannian Manifolds, SIAM Journal on Control and Optimization, vol.37, issue.2, pp.566-588, 1999. ,
DOI : 10.1137/S0363012995290744
On a general conception of duality in optimal control, Equadiff IV, pp.189-196, 1979. ,
DOI : 10.1016/0022-247X(70)90324-0
Riemannian manifolds: an introduction to curvature, 1997. ,
DOI : 10.1007/b98852
Introduction to smooth manifolds ,
The Projective SUMT Method for Convex Programming, Mathematics of Operations Research, vol.14, issue.2, pp.203-223, 1989. ,
DOI : 10.1287/moor.14.2.203
On the Riemannian Geometry Defined by Self-Concordant Barriers and Interior-Point Methods, Foundations of Computational Mathematics, vol.2, issue.4, pp.333-361, 2002. ,
DOI : 10.1007/s102080010032
Numerical Optimization, 2000. ,
DOI : 10.1007/b98874
Proximal point methods for quasiconvex and convex functions with Bregman distances on Hadamard manifolds, J. Convex Analysis, vol.16, issue.1, pp.49-69, 2009. ,
A Mathematical View of Interior-Point Methods in Convex Optimization, Society for Industrial and Applied Mathematics, 2001. ,
DOI : 10.1137/1.9780898718812
Convex Analysis, 1970. ,
DOI : 10.1515/9781400873173
Conjugate duality and optimization, Society for Industrial and Applied Mathematics, 1974. ,
Optimization techniques on Riemannian manifolds. Fields institute communications, pp.113-135, 1994. ,
Optimal Control with State-Space Constraint I, SIAM Journal on Control and Optimization, vol.24, issue.3, pp.552-561, 1986. ,
DOI : 10.1137/0324032
Convex Function and Optimization Methods on Riemannian Manifolds, 1994. ,
DOI : 10.1007/978-94-015-8390-9
Linear programming. Foundations and extensions, International Series in Operations Research & Management Science, 2001. ,
Convex Duality and Nonlinear Optimal Control, SIAM Journal on Control and Optimization, vol.31, issue.2, pp.518-538, 1993. ,
DOI : 10.1137/0331024
Globally Convergent Optimization Algorithms on Riemannian Manifolds: Uniform Framework for Unconstrained and Constrained Optimization, Journal of Optimization Theory and Applications, vol.55, issue.2, pp.245-265, 2007. ,
DOI : 10.1007/s10957-006-9081-0